Question

Two numbers are in ratio 5:6 . if 8 is subtracted from each of the number the ratio becomes 4:5 Find the number​

Answer 1

Let the 2 numbers be x and y

$\sf{According\:to\:the\:question,}$

$\sf{\dfrac{x}{y}= \dfrac{5}{6}}\\\\\\\longrightarrow \: \sf{6x = 5y}\\\\\longrightarrow \: \sf{x = \dfrac{5y}{6} \qquad \dashrightarrow [Equation\:1]}$

If 8 is subtracted, the ratio becomes 4:5.

$\sf{\dfrac{x-8}{y-8}= \dfrac{4}{5}}\\\\\\\\\implies \sf{5(x-8)=4(y-8)}\\\\\implies \sf{5x-40=4y-32}\\\\\longrightarrow \sf{5x - 4y = 40-32}\\\\\implies \sf{5x-4y=8 \qquad \dashrightarrow [Equation \:2]}$

Substitute Equation 1 in Equation 2,

$\sf{5x-4y=8}\\\\\implies \sf{5 \times \bigg(\dfrac{5y}{6}\bigg) - 4y=8}\\\\\\\implies \sf{\dfrac{25y}{6}-4y=8}\\\\\\\implies \sf{\dfrac{25y-24y}{6} = 8}\\\\\\\implies \sf{\dfrac{y}{6}=8}$

$\large{\boxed{\bf{\therefore \: y = 48}}}$

Substitute value of y in Equation 1,

$\sf{x=\dfrac{5y}{6}}\\\\\\\longrightarrow \sf{x = \dfrac{5 \times 48}{6}}\\\\\\\longrightarrow \: \boxed{\large{\bf{x = 40}}}$

Therefore the 2 numbers are 48 and 40

Answer 2

$\boxed{\huge{\sf{\star{AnswEr-:}}}}$

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☆ The two numbers are 40 and 48.

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$\large{\sf{\bigstar{Given\:,}}}$

☆ Two numbers are in Ratio-: 5:6

☆ If 8 is subtracted from each number ,

The ratio becomes -: 4:5

$\large{\sf{\bigstar{To\:Find\:,}}}$

☆ The number .

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$\huge{\sf{\bigstar{Solution \:,}}}$

》Let the two number be 5x and 6x

Then ,

Two numbers are in ratio -: 5x:6 x or $\frac{5x}{6x}$

Then ,

⊙ According to the question,

》 If 8 is subtracted from each of the number ,

Then ,

》The ratio becomes 4:5 or $\frac{4}{5}$

Then,

》$\frac{5x-8}{6x-8}=\frac{4}{5}$

[cross multiplication ❌]

》5(5x - 8) = 4(6x - 8)

》25 x - 40 = 24x - 32

[ Add 40 both side]

》25x - 40 + 40 = 24 x - 32 + 40

》25 x = 24x + 8

[Subtract 24 x from both side ]

》25 x - 24x = 24x + 8 - 24x

》 x = 8

Hence ,

☆ The two numbers are -:

First number -: 5x = 5 x 8 = 40

Second number-: 6x = 6 x 8 = 48

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